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On Optimal Cardinal Interpolation

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Abstract

For the Hardy classes of functions analytic in the strip around real axis of a size 2β, an optimal method of cardinal interpolation has been proposed within the framework of Optimal Recovery [12]. Below this method, based on the Jacobi elliptic functions, is shown to be optimal according to the criteria of Nonparametric Regression and Optimal Design.

In a stochastic non-asymptotic setting, the maximal mean squared error of the optimal interpolant is evaluated explicitly, for all noise levels away from 0. A pivotal role is played by the interference effect, in which the oscillations exhibited by the interpolant’s bias and variance mutually cancel each other. In the limiting case β → ∞, the optimal interpolant converges to the well-knownNyquist–Shannon cardinal series.

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Authors and Affiliations

  1. Dept. Math. and Statist., Queen’s Univ., Kingston ON, Canada

    B. Levit

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  1. B. Levit
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Correspondence to B. Levit.

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Levit, B. On Optimal Cardinal Interpolation. Math. Meth. Stat. 27, 245–267 (2018). https://doi.org/10.3103/S1066530718040014

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  • DOI: https://doi.org/10.3103/S1066530718040014

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